It's more of a survey than anything else, and deals with the open problem asking if there exists a solution to the 3X3 magic square whose entries are all distinct/unique perfect squares. I do include one original proof showing there cannot exist a 3X3 magic square of squares whose solution is, itself, a square.
Number Theory isn't really "my thing", though (like all math) I think it's an interesting field of study. It was kind of nice to get out of my geometry/topology...errr.mmm....space and write on something different (though I ended up using/invoking geometry anyway in the original proof showing no 3X3 magic square of squares has a square solution). I had fun writing it, and I hope you enjoy reading it.
I probably won't delve into the subject much more from here on out. I'm a horrible programmer, which is a necessary skill to have when tackling this problem (if you read the paper, you'll see just how HUGE the numbers you have to compute are!).
If you're interested in this open problem (or other magic square problems) I can't recommend Christian Boyer's page (multimagie.com) enough.
(Update:6/27/2019, 1:15 am) Notez Bien: In the original proof I provided showing there's no square solution to any 3X3 magic square of squares, it should be stated that the implication of the triangle argument is that for any unique triangle constructed with integer sides, at least one of the subsequently constructed triangles will be a permutation of the original (thus violating the "all entries are distinct integers" criteria).